A Multi-Objective Interpretation of Optimal Transport
将离散最优传输问题与一类多目标优化问题联系起来，通过帕累托效率和平衡解的概念建立一一对应关系，并讨论了正则化计算方法。
This paper connects discrete optimal transport to a certain class of multi-objective optimization problems. In both settings, the decision variables can be organized into a matrix. In the multi-objective problem, the notion of Pareto efficiency is defined in terms of the objectives together with nonnegativity constraints and with equality constraints that are specified in terms of column sums. A second set of equality constraints, defined in terms of row sums, is used to single out particular points in the Pareto-efficient set which are referred to as “balanced solutions.” Examples from several fields are shown in which this solution concept appears naturally. Balanced solutions are shown to be in one-to-one correspondence with solutions of optimal transport problems. As an example of the use of alternative interpretations, the computation of solutions via regularization is discussed.